PSI - Issue 40

N.A. Makhutov et al. / Procedia Structural Integrity 40 (2022) 264–274 Nikolay A.Makhutov at al. / Structural Integrity Procedia 00 (2022) 000 – 000

273

10

 

  



n an a к

 

(13)

 n n N N f f

where f n and

* an  are the frequency and amplitude of high-frequency loading stresses,

f , * a  , N - frequency, stress amplitude, and durability of the main low-frequency loading; κ n is the material characteristic. With the increase in the strength of the material (500 ≤σ u ≤1000 MPa), the value of κ n increases (0.9≤κ n <1.6). It is important for a liquid-propellant rocket engine that in an atmosphere of gaseous hydrogen the ductility of steels ψ cH in expression (12) decreases (Makhutov, 2011; Makhutov, 2013):

1   , 

(14)

h

m

1   

 

K p

cH c  

к 



H

H

H H

where K H is a characteristic of material sensitivity to hydrogen embrittlement, that depends on temperature (4≤ K H ≤ 6); p H is the pressure in a hydrogen environment; m H ≈0.15; h H ≈0.07 ÷ 0.08. For liquid-propellant rocket engines with increasing service life τ (from 70 to 5,000 s), it is necessary to take into account (Makhutov, 2008; Makhutov, 2011; Makhutov, 2017) the effect of time τ on the main mechanical properties ( σ у , σ u , ψ c ):                   m к y u к y u , , , , 0  . (15) where m τ is a material characteristic that increases exponentially with the increasing temperature t   T m m exp u u t u       0 . (16)

-3 to 6∙10 -3 , and the m

The value of β u τ increases with an increase in σ u from 5∙10

τ u value can be taken constant and

equal to 1∙10 -3 . The accumulated damage d in the i -mode of the cyclic loading (at amplitudes of stresses * with the number of cycles N i ) is estimated using the equation (12) and summated:

ai  and strains e ai and

(17)

 



 / i

d

N N

i

In the case of single-use rocket engines, the service life N s ≤ 25; for multiple use engines the total number of cycles can be increased up to N s ≤ 250. Performing calculations for the entire system of equations (1) - (16) makes it possible to establish safety factors for strength, plasticity, and service life characteristics, taking into account temperatures t , strain rate e , hydrogen pressure H , time τ :   maxs H u t ,e, p , n       ,   max , , , c H s e t e p n e    ,   s n H N N N ,N ,N ,N n   , (18) where σ max s , e max s , and N s are the maximum stresses, strains, and durability during operation. During the creation and operation of liquid-propellant rocket engines, these safety factors were gradually reduced and were established (Makhutov, 2008; Makhutov, 2011, Makhutov, 2017; Makhutov 2018) not lower than: n σ >1.1÷1.2; n e >1.5÷2.0; n N >2.5 ÷ 3. Further development of the outlined approach to the comprehensive analysis of performance and limit states of liquid-propellant rocket engines can be carried out only with the use of new complex technologies and systems with